‎Let $f:A\rightarrow B$ and $g:A \rightarrow C$ be two ring homomorphisms and let $J$ and $J^{'}$ be two ideals of $B$ and $C$‎, ‎respectively‎, ‎such that $f^{-1}(J)=g^{-1}(J^{'})$‎. ‎The bi-amalgamation of $A$ with $(B,C)$ along $(J,J^{'})$ with respect of $(f,g)$ is the subring of $B\times C$ given by‎ ‎$A\bowtie^{f,g}(J,J^{'})=\{(f(a)+j,g(a)+j^{'})‎/ ‎a \in A‎, ‎(j,j^{'}) \in J\times J^{'}\}.$‎ ‎In this paper‎, ‎we study the transference of $pm^{+}$‎, ‎$pm$ and finite character ring-properties in the bi-amalgamation.